March 2015 past paper solutions

[Ais_D]

Hi, does anyone have a worked a solution to the March 2015 past paper - model, audit and summary.
I worked on this all day yesterday but I'm struggling to understand how to calculate the E(x)'s and sum them over all years. Any help would be much appreciated.

 

[Steve Hales]

Which part of the project are you referring to?

 

[Ais_D]

The first part of the model - creating the E(x)'s. The instructions refer to summing over all years - what does the model look like?

 

[Steve Hales]

The first part of the model - creating the E(x)'s. The instructions refer to summing over all years - what does the model look like?

I'm sure that a model solution will be provided on the IFoA website eventually. In the meantime here's a way to start the project.

The Additional Guidance gives the full picture; starting with \(E(x)\) and progressing through to the total initial amounts exposed to risk \(E^{a^{*}}(x)\). These are the values given in the Exposure worksheet.

The expected claims are then equal to these total initial amounts exposed to risk multiplied by the probability of a claim occurring within each age band. The slight complication here is that the exposure data is split by age band, and the mortality table is split by age.

 

[ActStudent1405]

Thanks Steve for the tip. To convert the expected amount of claims by age band to expected amount of claims by age, I assumed an equal distribution of expected amount at each age. For example for age band 30-34, I divided the total expected claims amount in the age band by 5. This gave me the expected amount of claims at each age (an equal value at each age from 30 to 34 yrs), which I then multiplied by the given mortality rate to determine the expected amount of claims. Then, I summed the expected amount of claims at each age back into 6 age bands. Would this assumption be valid to answer part (iii) of the question?

 

[ActStudent1405]

Just a polite reminder to my previous question. Thanks

 

[Steve Hales]

To convert the initial amounts exposed to risk by age band to expected amount of claims by age, I assumed an equal distribution of exposure amount at each age. For example for age band 30-34, I divided the total initial amounts exposed to risk in the age band by 5. This gave me the expected amount of claims at each age (an equal value at each age from 30 to 34 yrs), which I then multiplied by the given mortality rate to determine the expected amount of claims. Then, I summed the expected amount of claims at each age back into 6 age bands. Would this assumption be valid to answer part (iii) of the question?

With a few minor alterations in bold, that sounds reasonable to me

 

[ActStudent1405]

Thanks Steve for your reply! Very helpful

 

[jjjkkk]

Am I right in thinking that the adjustment to the mortality table mentioned is just to multiply the qx's by the AvE ratio?

What is an acceptable method of implementing the recursive formulae in Excel?

Any help appreciated as sitting the exam this week

 

[Steve Hales]

Am I right in thinking that the adjustment to the mortality table mentioned is just to multiply the qx's by the AvE ratio?

That's what the instructions say in the Premium Calculation section

What is an acceptable method of implementing the recursive formulae in Excel?

An acceptable method is pretty much anything that can be easily understood by another user and is well documented. What did you have in mind?

 

[vikky]

Hi
I can get whole life assurance functions and annuity due functions on a spreadsheet.
I cant seem to get them for 10 year specfic terms.
The hint sheet equation is also not very helpful.
Can I please request for some help on this.
I am giving my exams fairly soon


 

 

[Steve Hales]

Hi
I can get whole life assurance functions and annuity due functions on a spreadsheet.
I cant seem to get them for 10 year specfic terms.
The hint sheet equation is also not very helpful.

You'll need to use a two-dimensional array for the recursive formula in the hint sheet because both variables x and n change with each update.